So, let me try and refine a few thoughts here.
1) The Original Constition, THe Constitution Refit, and the Constitution 2 are all seperate ships: increasing in power from oldest to youngest.
2) The Surya, Surya-Refit (Which is what the Reliant was), and the Miranda are all seperate ships: increasing in power from oldest to youngest.
Why i think as such.
1) IF the Enterprise was assigned to Academy Duty, why would they build/recristen the Enterprise-A. Also, why would that ship be used for such an important mission as to escort the chancellor of the klingon high council. As such i believe that the Constitution Refit and the Constition 2 are in fact very different in capability and power
2) Uniformity, i think all ships went through this process. The Federation, to the Federation-Refit, to the Star League....Saladin, to Saladin-Refit, to Siva, so and and so forth. I mean hell, look at the uniforms even. There was a comic i was browsing through, and Will Decker had come on baord the NON-REFITTED enterprise. He was wearing the Pajama uniforms (in fact scotty didnt like em), this means that while kirk was on his 5-year mission, many renovations were going on.
3) The Surya-Refit vs. The Connie-Refit. Yes i am of the belief, following this progression that the Reliant was indeed a Surya Refit, NOT a Miranda-class. Reasons why i think the RELIANT was a Surya-Refit:
A) it was assigned to a scientific team, not the front lines.
B) it would be outgunned by the ENT (see below)
C) again, progression of the TYPE-1 > TYPE-1-Refit > TYPE 2 scheme
This is mind, the Connie-refit should out-gun the Surya-Refit. The reason why it didnt in TWoK follow:
A) Trannee Crew on ENT
B) Hardened crew on REL
C) ENT was on Minimal power when it attacked the REL
D) the attaack was unexpected, and the ENT didnt have time to raise its shields.